The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is nonnegative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical...

Following a trend of sustained and accelerated growth, the VIXfutures and options market has become a closely followed, active andliquid market. The standard stochastic volatility models | whichfocus on the modeling of instantaneous variance | are unable to t theentire term structure of VIX...

We model the dynamics of asset prices and associated derivatives by considerationof the dynamics of the conditional probability density process for the value of an assetat some specied time in the future. In the case where the asset is driven by Brownianmotion, an associated \master equation"...

This paper derives an analytic expression for the distribution of the average volatility in the stochastic volatility model of Hull and White. This result answers a longstanding question, posed by Hull and White (Journal of Finance 42, 1987), whether such an analytic form exists. Our findings...

The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is nonnegative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical...

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...

We investigate the relationship between the gas spot market and the price of gas storage capacity. Contrary to the common belief, the auction prices for gas storage are mostly affected by the volatility of current market prices rather than by the winter-summer price differences. This paper...

When using an Euler discretisation to simulate a mean-reverting square root process, one runs into the problem that while the process itself is guaranteed to be nonnegative, the discretisation is not. Although an exact and efficient simulation algorithm exists for this process, at present this...

At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for...

The characteristic functions of many affine jump-diffusion models, such as Heston’s stochastic volatility model and all of its extensions, involve multivalued functions such as the complex logarithm. If we restrict the logarithm to its principal branch, as is done in most software packages,...